Soft decision Viterbi decoder for FSK demodulation under fast fading channel

In a soft decision Viterbi decoder, the log-likelihood ratio (LLR) metric is used to improve the performance of the error correction. However, this cannot be directly applied in frequency shift keying (FSK) wireless transmission system which uses a frequency discriminator for FSK de-modulation - an inherently non-linear circuit. The LLR for a linear system cannot be used for the FSK wireless transmission system. It is necessary to calculate LLR which considers the non-linear characteristic of the frequency discriminator. In this paper, we derive the modified LLR which considers the non-linear characteristic of the frequency discriminator. Simulation shows the effectiveness of the derived LLR for 4-ary FSK wireless transmission system.